Calculus and Linear Algebra. Vol. 2: Vector Spaces, Many-Variable Calculus, and Differential Equations

Wilfred Kaplan; Donald J. Lewis

doi:10.3998/spobooks.5597602.0002.001

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Calculus and Linear Algebra. Vol. 2: Vector Spaces, Many-Variable Calculus, and Differential Equations

Wilfred Kaplan; Donald J. Lewis

DOI: http://dx.doi.org/10.3998/spobooks.5597602.0002.001

Published by: Ann Arbor, MI: Michigan Publishing, University of Michigan Library, 2007.

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A-52 A-52 ANSWERS TO SELECTED PROBLEMS 2. 3, (1) _ 1, te t(t#0);A=2t(,0)(t#0);A=3t(3,4-.,)(t#04C). (a) A -- 1, K1 = Span (e1).VV/ = Span (ert e2); 1=2, K2=W,2=Span ((11.4,,1)). (c) A = 0, K0 )Sanl(e1 e9, iW0=V3. (e) A = 0, K0 Span (e1), W3) = V. Section 10-21, pa(ge 80'1 /0 10 2. (a) (2 9. (a) (1 1 0 0 0 0 0) 1 2 0 0 2 0 004 204 034 00} 00 2 -3, 04 4 ) 0 )1 0(c) 0 1 0 0 0 U 1( 00 J' 0 0 00 D 0 0 (c)/2 7 S1 -7 - (c) (1 1j K 0 1 0 0 0 0 7 1 -9 0 0 0) 0 1 0 0 1 0 0) B 0) 0 0) 1/ 0/ 1 1 0 0 0 0 1 0 0 0 01 Section 11-3, lpage 809 1. (a) 25, (c) 29, (e) -12, (g) 5, (1) 4. (e) a = y = </4, I3=:r/2. Section 11-5, page 817 Cos' 8 1. (a) Coincident. 2. (a)OPt'= (3, 5l) + t(-1,-5, 6),Q)on line, (c) OP' (4, -1, 5) + t(2' 3, - 8), Qot on line. 3. (a) Skew, (c) meet at (1, 1, 1). 4. (a) Collinear, (c) collinear. 5. (a) N'ot orthogonal, (c) not orthog;onal, (e) orthiogonal. 6. (ra)}Cos16 16(1, (c) C os..5/ 25 9.. (a)(2 ) (c)( it,3,>,and ',,0) Section 11-9, page 8S29) 1. (a) 12i ~ 41k, (c) 4, (e) 4, (g) {ii -.18 +k, (i)--41- 4j~+12 k. 3. (a) Par allel, nonncoincident, (c) skiew. 8. (a) Negativec, (e) positive, (e) linearly depiendet.

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